Primaries and Candidate Polarization: Behavioral Theory ...woon/papers/woon-primaries-aug17.pdf · Abstract Do primary elections cause candidates to take extreme, polarized positions?

Primaries and Candidate Polarization: BehavioralTheory and Experimental Evidence

Jonathan Woon∗

University of Pittsburgh

August 23, 2017†

Abstract

Do primary elections cause candidates to take extreme, polarized positions? Standardequilibrium analysis predicts full convergence to the median voter’s position, but be-havioral game theory predicts divergence when players are policy-motivated and haveout-of-equilibrium beliefs. Theoretically, primary elections can cause greater extrem-ism or moderation, depending on the beliefs candidates and voters have about theiropponents. In a controlled incentivized experiment, I find that candidates diverge sub-stantially and that primaries have little effect on average positions. Voters employ astrategy that weeds out candidates who are either too moderate or too extreme, whichenhances ideological purity without exacerbating polarization. The analysis highlightsthe importance of behavioral assumptions in understanding the effects of electoral in-stitutions.

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∗Associate Professor, Department of Political Science, Department of Economics (secondary), and Pitts-burgh Experimental Economics Laboratory, [email protected], 4443 Wesley W. Posvar Hall, Pittsburgh, PA,15260†Thanks to Keith Dougherty, Sandy Gordon, Greg Huber, Scott Moser, Charlie Plott, Danielle Thom-

sen, Alan Wiseman, participants at the Yale CSAP American Politics Conference, seminar participants atWashington University in St. Louis, University of Oxford (Nuffield College CESS), IC3JM (Juan MarchInstitute), and the Pittsburgh Experimental Economics Lab for helpful comments and feedback. I am alsoindebted to Kris Kanthak for vigorous discussions during the early stages of this project. Previous versionsof the paper were presented at the 2014 Annual Meeting of the American Political Science Association, the2016 Public Choice Society Meeting, and the 2016 Midwest Political Science Association Conference. Thisresearch is supported by the National Science Foundation under Grant No. SES-1154739 and was approvedby the University of Pittsburgh Institutional Review Board under protocol PRO14060001.

The partisan primary system, which favors more ideologically pure candidates,has contributed to the election of more extreme officeholders and increased po-litical polarization. It has become a menace to governing.

— Sen. Charles Schumer (D-NY)1

The divergence between candidates and legislators from the two major parties is an

enduring feature of the American political landscape (Ansolabehere, Snyder and Stewart

2001, Bonica 2013, Poole and Rosenthal 1984, 1997), and the fact that polarization is at

historically high levels is a significant concern for scholars and observers of democratic gov-

ernance, representation, and public policy (Hacker and Pierson 2006, Mann and Ornstein

2013, McCarty, Poole and Rosenthal 2006, 2013). Indeed, politicians and the popular press

often lay much of the blame for this phenomenon on partisan primary elections, typically

employing a simple, intuitively appealing argument: Candidates take extreme positions be-

cause they must appeal to partisan primary voters, whose preferences are more extreme than

those of voters in the general election.

Political scientists have tested this argument, finding that while there is some evidence

to suggest that primary elections promote extremism, the empirical record is generally mixed.

Extremists are more likely to win congressional primaries than moderates (Brady, Han and

Pope 2007), and legislators elected under closed primaries take more extreme positions than

legislators elected under open primaries (Gerber and Morton 1998). But other analyses find

that polarization is largely unrelated to the introduction of direct primaries (Hirano et al.

2010) and to the variation in the openness of primaries across states (McGhee et al. 2014).

At best, primaries may cause polarization under limited circumstances (Bullock and Clinton

2011), and despite the divergence of candidate positions, general elections nevertheless exert

nontrivial pressure on candidates to moderate (Hall 2015, Hirano et al. 2010). These findings

seem puzzling in light of the basic theory of representation at the heart of this literature:

that the preferences of primary electorates should affect the preferences of party candidates.

1Charles E. Schumer, “Adopt the Open Primary,” New York Times, July 21, 2014.

1

How, then, should we understand the causal relationship between primary elections

and candidate positioning? I examine the connection, both theoretically and experimen-

tally, by comparing elections with and without primaries while holding other features of the

electoral environment constant, including preferences and information. The analysis focuses

on a particular aspect of primary elections—how the introduction of voters in the candidate

selection process affects strategic competition between parties—while abstracting away from

many other considerations that might also affect polarization.2

The theory that I develop suggests a more nuanced relationship between primaries

and polarization than portrayed in the existing literature. I show that primaries can cause

polarization or moderation, depending on candidates’ beliefs about opposing voters’ strategic

behavior—even when preferences are held constant. To generate this insight, I rely on ideas

from behavioral game theory, which retains much of the theoretical apparatus from standard

game theory while allowing for key departures (Camerer 2003). Specifically, I allow players

to have “incorrect” or “non-equilibrium” beliefs about others’ actions (Crawford, Costa-

Gomes and Iriberri 2013), but assume they are nevertheless strategic in the sense that they

best respond to what they think other players do (Camerer, Ho and Chong 2004, Nagel

1995, Stahl and Wilson 1995). The analysis demonstrates that changes in preferences alone

are insufficient to cause polarization. Instead, beliefs and expectations about the strategic

behavior of others play important roles in conditioning the effect of institutions.

I turn to the laboratory and conduct a series of experiments to test the effects of

primaries on candidate positions. The chief advantage of the laboratory for theory testing is

control (Aldrich and Lupia 2011, Falk and Heckman 2009, Morton and Williams 2010), so

we can be confident that the observed behavior occurs under the same conditions specified

by the theoretical model. Indeed, subjects face the same key trade-off in the experiment as

the actors do in the model between increasing the favorability of winning outcomes versus

increasing the probability of winning. In the lab, theoretically-relevant quantities of interest

2Such considerations include candidate valence, turnout, activists, or campaign contributions (Adamsand Merrill 2008, Callander and Wilson 2007, Hirano, Snyder and Ting 2009, Hummel 2013, Meirowitz 2005,Snyder and Ting 2011). 2

that are difficult to measure using observational data with any accuracy or without strong

assumptions (in particular, preferences and positions) are also known exactly. Furthermore,

experimental manipulations permit tests of mechanisms not possible using observational

data. Thus, laboratory experiments are ideal for theory testing given their high internal

validity.3

The key finding from the experiment is that primaries appear to cause a kind of

ideological purity rather than greater extremism. I find that subjects take positions that

diverge significantly from the median voter’s position, regardless of whether or not there is

a primary. This finding lends support for the behavioral theory. However, the extent to

which primaries cause polarization is limited. Greater polarization only occurs when there

is no feedback such that candidates cannot learn about the behavior of others, and this

polarization happens because voters tend to select extremists over moderates, even though

candidate positions do not vary with the election format. More precisely, the analysis reveals

that voters support neither party extremists nor party moderates unconditionally. Instead,

they select candidates with intermediate positions—consistent with their own subjective

beliefs about optimal candidate positions, which tend to be approximately halfway between

the median voter and their own party’s ideal point. This behavior generates a greater

concentration of candidate positions around an average that diverges from the median voter.

Hence, greater ideological purity reinforces, rather than exacerbates, polarization.

3The main question of interest for theory testing, as Aldrich and Lupia (2011, 90) put it, is “Will peoplewho are in the situations you describe in your model act as you predict?” Also see Dickson (2011), Palfrey(2006), and especially, Morton and Williams (2010). While the question of external validity (“to what extentcan we generalize from a particular sample?”) is an enduring source of controversy in political science, Falkand Heckman (2009) argue in their insightful defense of the value of lab experiments in social science that“Behavior in the laboratory is reliable and real: Participants in the lab are real human beings who perceivetheir behavior as relevant, experience real emotions, and take decisions with real economic consequences”(536). Indeed, there are many precedents for testing theories of elite behavior using laboratory experiments(e.g., Aragones and Palfrey 2007, Frechette, Kagel and Lehrer 2003, Morton 1993). Moreover, Druckmanand Kam (2011) note that there is nothing inherently problematic with using student samples, and there islittle evidence to suggest that using undergraduates as stand-ins for elites biases the results in any particulardirection (see Morton and Williams 2010, 343–347). For example, Potters and van Winden (2000) findsignificant, but small, differences between students and lobbyists, Fatas, Neugebauer and Tamborero (2007)find elites do not fit prospect theory as well as students, while studies by Belot, Duch and Miller (2015),Cooper et al. (1999), and Mintz, Redd and Vedlitz (2006) suggest that student samples provide a lowerbound to departures from rational decisionmaking.

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Related Literature

My analysis follows a long tradition of using spatial voting models to understand elections.

Although existing spatial models (Aronson and Ordeshook 1972, Coleman 1972, Owen and

Grofman 2006) predict candidate divergence in elections with primaries (two-stage elections),

they do so in isolation and do not compare them explicitly to elections without primaries

(one-stage elections).4 These models also assume that general election outcomes are proba-

bilistic, which is theoretically consequential because the mechanism they rely on to produce

divergence is the combination of policy-motivations and uncertainty about which candidate

will win the general election—the same forces that generate incentives for candidate diver-

gence in the absence of primaries (Calvert 1985, Wittman 1983). Thus, it is unclear from the

literature whether polarization can be traced to any distinctive features of primaries per se,

as electoral institutions. By explicitly comparing institutions, my analysis speaks directly to

the connection between primaries and polarization.

Existing theoretical models of two-stage elections also typically maintain the assump-

tion that all political actors, candidates as well as voters, are strategic and forward-looking

(e.g., Owen and Grofman 2006). Several models consider the issue of raiding and cross-over

voting in open primaries (Cho and Kang 2014, Chen and Yang 2002, Oak 2006), which re-

quires a fairly high degree of strategic sophistication, but this kind of behavior is outside the

scope of my analysis. My results also differ from Adams and Merrill (2014), who find that

strategic versus expressive voting both generate divergence, but in their model candidates

are office-motivated and vary in their campaign skills. In contrast to the preponderance of

existing formal models, I take a behavioral (i.e., bounded rationality) approach advocated

by Simon (1955), Ostrom (1998) and others. I do so by explicitly allowing for sincere or

myopic behavior as well as subjective beliefs that are inconsistent with observed behavior.

4An exception is Jackson, Mathevet and Mattes (2007), who compare alternative nomination systemsin a citizen-candidate framework. In their model, primary elections affect whose preference is decisivein nominating candidates and have no effect if party leaders and the median party voter have the samepreferences. Other formal models of primary elections largely focus on considerations of voter uncertainty,incomplete information, and signaling along with issues of candidate valence and distributional concerns.

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This paper is also related to two distinct literatures in experimental political science.

The experimental literature on candidate positioning in two-party elections finds a strong

tendency for candidates and election outcomes to converge to the median voter’s position and,

more generally, to the Condorcet winner under a variety of conditions, including incomplete

information (Collier et al. 1987, McKelvey and Ordeshook 1982, McKelvey and Ordeshook

1985). An exception is when candidates are ideological and voting is probabilistic (Morton

1993). The other related literature, on strategic voting, generally finds little (or at best,

mixed) evidence for voter sophistication in the early stages of a multi-stage voting agenda

or election contest (Cherry and Kroll 2003, Eckel and Holt 1989, Herzberg and Wilson 1988,

McCuen and Morton 2010, Plott and Levine 1978, Van der Straeten et al. 2010).5 Taken

together, these previous studies raise doubts that voters will be highly strategic (even if

candidates are), calling into question theories predicated on voter rationality and strategic

sophistication.

Theoretical Framework and Analysis

I consider an environment with two parties, Party L and Party R, competing to win a single

office. Candidates choose positions in a one-dimensional policy space, and the winning

candidate’s position is implemented as the policy outcome. In the electorate, there are an

equal number of voters in each party and a set of independent, non-partisan “swing” voters.

Candidates and voters alike are entirely policy-motivated, caring only about the location of

the policy outcome w ∈ R. The incentive to win office is therefore purely instrumental in

this model, which departs from usual Downsian office motivations. Parties are completely

homogeneous in that candidates and voters belonging to the same party are identical and

have the same ideal point. Thus, there are three ideal points: θL for members of Party L, θR

5An exception is Smirnov (2009), who studies endogenous agendas and finds behavior consistent withsophisticated expected utility maximization. There is stronger experimental evidence for other kinds strategicvoting, however, such as coordinating on a less-preferred candidate in multi-candidate contests (Rietz 2008),and in incomplete information pivotal voter settings (e.g., Battaglini, Morton and Palfrey 2010).

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for members of Party R, and θM for the electorate’s median voter, where θL < θM < θR. I

assume that preferences are symmetric and single-peaked. Specifically, in the experimental

implementation, all actors have linear loss utility functions, ui(w) = K − |w − θi|, for

i ∈ {L,M,R} and some constant K. Preferences are also common knowledge, so the election

takes place under conditions of complete information.

There are two types of elections. In one-stage elections (1S), there is one candidate

from each party whose positions are cL and cR, respectively, and one round of majority rule

voting to select the winning candidate. In two-stage elections (2S), there are two candidates

from each party (denoted cL1 and cL2 from Party L, cR1 and cR2 from Party R) who compete

in an intra-party first round election (the “primary” election). The two candidates who

win their respective party primaries then compete in a second round election (the “general”

election) to select the winning policy w. In other words, the parties hold simultaneous

“closed” primaries so that the voter with ideal point θL effectively chooses cL ∈ {cL1, cL2}

in the Party L primary at the same time that the voter with ideal point θR chooses cR ∈

{cR1, cR2} in the Party R primary. In the general election, the median voter with ideal point

θM chooses the election outcome from the two candidates selected by the parties’ respective

median voters, w ∈ {cL, cR}.

To generate predictions about candidate positioning and to identify the potential ef-

fects of the election format, I consider a variety of alternative behavioral assumptions. I

begin with standard game theoretic analysis, applying Nash equilibrium as the standard so-

lution concept. Because I am interested in making behavioral predictions, the interpretation

of Nash equilibrium is worth a brief discussion. One way to interpret Nash equilibrium is

to think of it as an idealized set of assumptions such that actors are not only fully rational

but also that their rationality is common knowledge (Aumann and Brandenburger 1995). In

this interpretation, we can think of political actors as forming beliefs about others’ current

and future behavior that are fully consistent with players’ actual strategies and behavior.

Alternatively, Nash equilibrium can be interpreted as merely representing a stable outcome

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in which strategies are mutual best responses without necessarily invoking an epistemic or

belief-based justification of how individuals make decisions in games. Such an approach,

however, does not make clear cut predictions about how games are played before an equi-

librium state is reached. Nevertheless, under a wide variety of learning models, experience

can lead play to converge to Nash equilibrium (Fudenberg and Levine 1998), and the role of

experience can be investigated experimentally.

Relaxing the Nash assumption of the mutual consistency of beliefs and actions gen-

erates an interesting variety of behavioral possibilities. In my analysis, I first explore the

implications of voter sophistication for candidate positioning while holding candidate ra-

tionality constant. If voting is “sincere,” then primary elections produce more polarized

candidates than voting that follows an equilibrium strategy. I then consider another de-

parture from standard assumptions: beliefs that some players make mistakes in choosing

their positions. They might do so for any number of reasons, such as micalculating the opti-

mal position, misjudging or underestimating the rationality of others, or having preferences

over outcomes of the game that are not fully captured by their material payoffs. Strate-

gically sophisticated players, recognizing that there are other players who make mistakes,

will then choose positions that differ from the Nash predictions—in the direction of their

parties’ ideal points—but that are optimal given their own beliefs about the distribution of

opponents’ positions. Introducing noise or the possibility of mistakes generates divergence

in both one-stage and two-stage elections.

With noise, the effect of introducing a primary election is also more complicated.

Similar to the case in which candidates do not make mistakes, the optimal positions de-

pend critically on voting behavior. If voters always choose moderate primary candidates,

then two-stage elections will generate greater convergence of candidate positions than in

one-stage elections. However, if voters always choose more extreme primary candidates,

then candidates in two-stage elections will be more polarized than candidates in one-stage

elections. There is also a third possibility. If voters form their own beliefs about the position

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most likely to maximize their expected utility and vote for candidates closest to this position,

then the degree of candidate divergence in two-stage elections is increasing in what we might

call voters’ belief-induced ideal points. Furthermore, there exists a belief-induced ideal point

such that candidates’ optimal positions diverge from the median voter by the same amount

in both one-stage and two-stage elections. Behavioral game theory thus establishes a critical

link between the effect of primaries and candidates’ beliefs about opponents’ primary voting

behavior.

Candidate equilibrium with fully strategic voters

Equilibrium theory makes identical predictions for both one-stage and two-stage elections: In

any equilibrium, the winning candidate’s position is the median voter’s ideal point. In one-

stage elections, the logic is straightforward. The median voter chooses the party candidate

closest to his or her ideal point as the winning candidate, so if one candidate adopts θM

as a campaign position, no other position can defeat it. In the unique equilibrium of the

one-stage election game, both parties’ candidates must choose cL = cR = θM . If not, either

the winning party’s candidate could do better by finding a position closer to her ideal point

while still winning the election or the losing candidate can find a position that wins the

election, thereby obtaining a better policy outcome for herself. Thus, w = θM is the unique

equilibrium policy outcome.

In two-stage elections, the outcome is the same, but the equilibrium strategies of the

primary voters must be specified. Given a set of candidate positions and voters’ expecta-

tions that the general election median voter will choose the more moderate of the parties’

candidates, a primary voter’s strategy is to choose the candidate closest to her ideal point

as long as she believes the candidate will also win the general election (and in equilibrium,

the voter’s beliefs about which candidate will win are correct). Because candidates and

voters have the same preferences, the incentives guiding optimal candidate strategies in the

one-stage election are similar to those that guide rational voting behavior in two-stage elec-

8

tions: if offered the same choices, candidates and voters would choose the same position (the

only difference is that candidates can choose any position while primary voters’ choices are

constrained).

In any equilibrium of the two-stage election game, there must be at least one candidate

from each party located at θM , so primary voters will always be observed choosing the

moderate candidate along the path of play. If so, both parties’ primary voters will select

a candidate at the median voter’s ideal point and the policy outcome is therefore w = θM .

Ruling out other possible outcomes then follows from the same logic as in the nonprimary

election. Fully strategic behavior from voters predicts full convergence to the median voter’s

position in both one-stage and two-stage elections.

Prediction 1. If voters and candidates are rational, forward-looking agents and form correct

beliefs about others’ behavior, then (a) the moderate candidates from each party will adopt the

median voter’s position and (b) primaries will have no effect on the polarization of candidates

in the general election.

Candidate equilibrium with sincere voters

I next consider the possibility that primary voters are myopic and vote “sincerely.”6 I assume

that sincere voters simply vote for the candidate closest to their ideal points, so they are

myopic in the sense that they fail to recognize that the candidate’s chances of winning the

general election affect the policy outcome (and hence their payoffs). With myopic voters, the

two-stage election game has multiple equilibria in which candidates take divergent positions

while the equilibrium of the one-stage election game remains the same (full convergence,

since there are no primary voters).

6While the overall level of voter “rationality” remains an ongoing subject of debate, the assumptionthat voters are myopic is consistent with recent observational and experimental research (e.g., Healy andMalhotra 2009, Huber, Hill and Lenz 2012, Woon 2012). A theory of elections with boundedly rational,behavioral voters is also worked out by Bendor et al. (2011).

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In any equlibrium of the two-stage election game with sincere voters, candidates

within each party must adopt the same position, and opposing party candidates must be

equidistant from the median voter. Specifically, an equilibrium is characterized by the con-

dition that cL1 = cL2 = θM − δ and cR1 = cR2 = θM + δ, where δ > 0 denotes some amount

of divergence between candidates. The median voter’s strategy is to select the candidate

closest to her own ideal point, breaking ties in favor of each party with equal probability.7

The result of the general election is therefore a lottery over w ∈ {θM − δ, θM + δ}, and the

expected value of the outcome is the median voter’s position, E[w] = θM . Any candidate

who adopts a more extreme position would, at best, be able to win their own primary but

then would lose the general election with certainty. Moving to a more moderate position

would not change the result of the primary and thus would not change the general election

result either. Since no candidate can obtain a better policy outcome by unilaterally adopting

a different position, campaign promises characterized by intra-party convergence and inter-

party symmetric divergence constitute an equilibrium of the primary election game with

sincere voters. The basic intuition underlying this result is that because of sincere primary

voters, intra-party competition limits any one candidate’s ability to moderate their party’s

position in the general election. Thus, in contrast to full convergence in one-stage elections,

any amount of divergence can be supported in two-stage elections.

Prediction 2. If candidates are rational and forward-looking but primary voters “sincerely”

select candidates closest to their own ideal points, then (a) candidates from each party will

take positions that diverge from the median voter by the same amount in two-stage elections,

and (b) winning candidates will be weakly more polarized in two-stage elections than in one-

stage elections.

7Note that it is also possible to construct equilibria in which the median voter has a bias for one ofthe parties (i.e., breaks ties in favor of one party rather than randomizing), but this would not affectthe equilibrium positions of the candidates. Thus, even though the random tie-breaking rule matches theexperimental setup, it is not necessary for the results.

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Candidate best responses to out-of-equilibrium beliefs

The previous sections assumed that candidates correctly anticipate whether voters use Nash

or sincere voting strategies and that their beliefs about other candidates are consistent with

those candidates’ actual behavior. That is, if candidate j chooses the platform cj, then

candidate i must believe with certainty that cj must really be j’s position. However, this

mutual consistency of candidates’ beliefs and actions might break down in a number of ways.

Candidates are likely to face cognitive constraints, they may engage in incomplete strategic

reasoning, or they may doubt the rationality of other candidates. In this section, I apply

the notion of limited strategic sophistication motivated by level-k models in behavioral game

theory (Crawford 2003, Nagel 1995, Stahl and Wilson 1995), positing that candidates have

some (possibly arbitrary) beliefs and analyze the best response to such beliefs.8

To model this, let candidate i’s beliefs about the positions of candidates from the

opposing party j 6= i be given by the cumulative distribution F (cj). Importantly, these beliefs

need not be accurate. For instance, if j’s true position is cj = 0, candidate i might believe

that cj is uniformly distributed between −1 and 1. We can think of the distribution F (cj)

as representing subjective beliefs that will typically not satisfy the equilibrium consistency

requirement.9

By relaxing the standard equilibrium assumption of belief consistency, an otherwise

expected utility maximizing candidate will choose a position that diverges from the median

voter’s ideal point. The reasoning is as follows. If a candidate believes there is some possibil-

ity that the opposing candidate’s position diverges from the median voter, then it cannot be

optimal for a policy-motivated candidate to choose a platform exactly at the median voter’s

ideal point. Instead, the candidate will choose a position that trades off some probability of

8While level-k models are a subset of the class of models that assume out-of-equilibrium beliefs, mytheory does not rely on different levels of sophistication or reasoning as modeled explicitly in the level-kframework.

9I assume that the PDF f(cj) has full support over the interval between median voter θM and theopposing party θj . The distribution F (cj) can also be interpreted as an objective probability distribution ifcandidates’ choices are noisy and F (cj) reflects the true distribution of candidate positions.

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EUHcRL

EUeHcRL

cRecR

*cRm

EUmHcRL

Positions

Figure 1: Comparison of candidate expected utility in one-stage and two-stage elections asa function of non-equilibrium beliefs and opponents’ primary voting

winning against potential policy gains obtained from choosing a position closer to his or her

own ideal point. When a candidate is more likely to expect her opponent to be extreme (i.e.,

when F (cj) puts more weight on extreme positions), then she herself will take a position with

greater divergence from the median voter in response. To illustrate this concretely, suppose

that θR = 1, the left party’s ideal point is θL = −1, the median is θM = 0, and F (cL) is a

uniform random variable, cL ∼ U [−1, 0]. With linear loss utility, the optimal position that

balances this trade-off is c∗R = 13. This is illustrated by the solid line in Figure 1 showing the

expected utility function EU(cR).

Next, I consider how these beliefs about opposing candidates’ positions interact with

the election format. The main result is that the effect of primaries will depend on the

candidates’ beliefs about the opposing party’s primary voters. The baseline for comparison

is a one-stage election with opponents drawn from the belief distribution F (cj). For the

purposes of exposition, suppose that F (cj) is uniform as in the example just given and as

shown in the left side of Figure 2, so the candidate’s best position is the one that maximizes

the expected utility function shown by the solid line in Figure 1.

In a two-stage election, it is not the original distribution of candidates F (cj) that

matters, but beliefs about which candidate will emerge from the primary election. Let

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G(cj) denote this latter set of beliefs about the candidate selected by the opposing party’s

primary—the candidate that i expects to face in the general election. Intuitively, we can

think of the primary election as a selection mechanism or filtering process that affects whether

a party’s candidate is systematically more or less extreme than the party’s initial set of

candidates.

More precisely, suppose that both of the opposing party’s candidates are indepen-

dently drawn from F (cj). Now consider how primary voting behavior affects G(cj) and, in

turn, candidates’ positions. If j’s primary voters unconditionally select the more extreme

candidate (as they would if they voted sincerely), then party j’s candidate in the general

election will be the more extreme of two independent draws from F (cj). This results in a

distribution G(cj) that is skewed more towards j’s own ideal point than F (cj), as shown by

the triangular distribution in the upper-right of Figure 2 when F (cj) is uniform. When vot-

ers choose extremists, primaries generate incentives for greater extremism than in one-stage

elections, as illustrated by the upper-dashed expected utility function EU e(cR) in Figure 1.

The flip-side of this is that if j’s primary voters select the more moderate candidate (as

they would in equilibrium, they generate incentives for greater moderation than in one-stage

elections. This is because party j’s general election candidate will be the more moderate of

two independent draws from F (cj), resulting in a distribution of beliefs G(cj) that is skewed

more towards the median voter than F (cj), as shown by the triangular distribution on the

bottom-right of Figure 2. When the probability of facing an extremist opponent is lower,

a candidate must moderate their position in response, which is shown by the lower-dashed

expected utility function EUm(cR) in Figure 1.

These are not the only possibilities, as primary voters might also behave in other

ways. For example, a fairly sophisticated voter might reason in the same way as a candidate

and form the same beliefs G(ci) based on expectations about opposing primary voters. To

generalize this a bit, suppose that a voter has a belief-induced ideal point c∗j and always votes

for the candidate in the primary whose position is closest to c∗j ; sometimes this will be the

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L M L M

L M

L MR Distribution of candidates

in first stage and one-stage elections

Distribution of candidates in second stage after selection by

primary voters

If voters select

candidate closest to L

If voters select

candidate closest to M

If voters select candidate closest to !!!

!

Figure 2: Comparison of beliefs in one-stage and two-stage elections as a function of oppo-nents’ primary voting behavior

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moderate and sometimes the extremist. The result is a distribution of primary candidates

G(cj) that has greater mass closer to c∗j than F (cj) does. If c∗j happens to be the midpoint

between the voter’s ideal point and the median voter, G(cj) will be the symmetric triangular

distribution in the middle-right of Figure 2. Note that while the mean of this distribution

is the same as the original distribution F (cj), it has lower variance. Primary elections may

therefore also have the effect of reinforcing a kind of ideological purity even when there is

no discernible effect on average candidate positions.

In contrast to standard equilibrium analysis, which predicts full convergence, a sim-

ple model with non-equilibrium beliefs generates divergence in candidate positions, even in

the absence of primaries and with complete information about preferences. Moreover, the

effect of primaries varies with candidates’ expectations about the opposing party’s voting

behavior. Primaries can indeed cause greater polarization, but only if primary voters select

sufficiently extreme candidates. They can also cause greater moderation, if primary voters

select moderates.

Prediction 3. If candidates have non-equilibrium beliefs about the distribution of opposing

candidates, then (a) candidate positions will diverge from the median voter’s ideal point in

both one-stage and two-stage elections, (b) the direction of the effect of primary elections on

candidate polarization depends on expectations about voting behavior, and (c) polarization

in two-stage elections is increasing in the expected extremity of candidates selected by the

opposing party’s primary voters.

Experimental Analysis

The theoretical analysis generated a set of competing predictions about the effect of primaries

as a function of alternative behavioral assumptions. If all players are fully strategic, then

we should observe full convergence to the median voter’s position and primaries should have

no effect. If candidates are strategic but voters are not, then we should observe candidate

15

divergence in two-stage elections but not one-stage elections. If the behavioral theory has

merit and candidates have subjective beliefs about their opponents’ positions, then either

polarization or moderation is possible depending on voter behavior. Which set of assump-

tions better reflects human behavior is ultimately an empirical question, and thus, I turn to

the lab.

Procedures

The experiment was conducted at ******** and involved a total of 182 participants drawn

primarily from the university’s undergraduate population. Each session involved 14 par-

ticipants, and each subject participated in one session of either the one-stage (1S) election

treatment (6 sessions) or the two-stage (2S) election treatment (7 sessions). At the beginning

of each session, following standard laboratory procedures, subjects gave informed consent,

the instructions were read out loud to induce public knowledge, and subjects answered a set

of questions about the rules on their computers to ensure comprehension.10 The interface

was computerized and programmed using the software z-tree (Fischbacher 2007). Each ses-

sion took about about an hour and a half to complete, and subjects earned an average of

$21.10 (including a $7 show-up fee).

Subjects participate in a total of 40 elections, and the instructions emphasize that

each election is to be treated as a “separate decision task.” For each election, subjects are

divided into two groups of seven participants, and every member of a group has the same

payoff function and ideal point.11 Throughout the experiment, the policy space is the set

of integers from 1 to 200, and payoffs are given by the linear loss function 200− |w − θi|.12

10See the Appendix for the full text of the experimental instructions. Comprehension of the instructionswas high. The percentage of correct responses for individual questions ranged from 81% to 94%, and69% answered all 4 questions correctly while only 8% missed more than one question. These figures likelyunderestimate the overall degree of comprehension since subjects read explanations of the correct answersbefore playing the game.

11We can think of each group as a party, although I am careful to avoid using the term “party” whendescribing the game to subjects. Groups were randomly reassigned between rounds in two sessions of eachtreatment, while the remaining sessions involved fixed groups. The method of group assignment does notaffect the results, so I ingore the distinction and pool the data in the analysis.

12Note that with a linear loss function (in contrast to quadratic loss), every possible policy outcome

16

The parties’ ideal points are located symmetrically from the median voter’s ideal point θM

such that θL = θM − δ, θR = θM + δ, and δ ∈ {50, 75}. The numerical value of θM varied

from election to election, while the exact sequence of values is identical across sessions and

treatments.13 Payoffs are denominated in “points” and converted to cash by dividing by 10

and rounding to the nearest quarter; each election is worth between $0 and $20 dollars. The

final payment is determined by randomly selecting one election to count for payment and

adding the show-up fee.

At the beginning of the election period, subjects first learn the position of every

player’s ideal point. Every subject then chooses a “campaign promise” (their policy position),

and they know that if their campaign promise is selected as the winning position, it will affect

every other subject’s payoff. After subjects choose their campaign promise, the computer

then randomly selects candidates from each group: one candidate from each group in the

1S election and two candidates from each group in the 2S election, with each group member

equally like to be selected and the selection of candidates independent across election periods.

The rest of the subjects are assigned to the role of a voter in that election. Thus, at the

beginning of each election, every subject is a potential candidate and does not know whether

he or she is a candidate until after submitting a campaign promise.14

Once the candidates are selected, the game proceeds to the voting stages. In the 2S

election, voters first choose between one of their group’s two candidates by majority rule.

Each primary (first stage) vote is held simultaneously, and neither party knows the positions

of the other group’s candidates while voting. Abstentions are not allowed. After each group

between the parties’ ideal points generates an equal amount of total social welfare, making it unlikely thatrisk neutral, altruistic subjects will want to choose the midpoint between parties to maximize the total socialmonetary payoffs of both groups. However, to the extent that subjects’ preferences for money exhibit riskaversion (and they expect this of other subjects), total social welfare will be maximized at the midpointbetween parties, which would bias the results toward median convergence.

13To determine the sequence of values, I randomly selected the median’s position, θm, from the integersbetween 51 and 150 for δ = 50 and between 76 and 125 when δ = 75. I varied the numerical values in orderto encourage subjects to pay attention and think about their relative, rather than absolute, positions.

14This method of role assignment is similar in spirit to the strategy method and maximizes the numberof observed positions in the experiment given that one of the primary goals of the experiment is to measureand test candidate positioning behavior.

17

selects its nominee, a second round of voting takes place to choose the winning policy from

the two groups’ nominees. All voters participate in this second round, which is effectively

the “general election.”15 In contrast to the 2S election treatment, the 1S election treatment

features only one round of voting in which every voter participates.

The median voter in the general election in both the 1S and 2S election treatments is

a “computer voter” who has a distinct ideal point and, as the instructions explain to subjects

(following Morton 1993), is “like a robot programmed to always vote for the candidate whose

campaign promise gives it the higher payoff value.” In the case of ties, the computer votes

for each candidate with equal probability. The subjects are informed of the computer voter’s

ideal point before every election.

The 40 elections within each session are divided into two parts, with each part varying

the type of feedback subjects receive. Part 1 consists of 10 elections without any feedback.16

Part 2 consists of 30 elections with feedback provided to subjects after each election. The

information subjects receive includes the positions of the subjects who were selected as

candidates, the number of votes for each candidate, the winning position, and the payoff

from the final outcome. In the first half of the elections in each part, the left and right

groups’ ideal points are 100 units apart, while they are 150 units apart in the second half of

the elections. Note that these two within-subjects manipulations vary ancillary assumptions

(feedback and distance between ideal points) and therefore serve as robustness checks. The

experimental manipulation of theoretical interest is the between-subjects manipulation of

the electoral institution.

15To avoid priming subjects’ political attitudes regarding primaries, I avoid referring to the two roundsof voting as a “primary” and “general” election but instead refer to them as the “first voting stage” and the“second voting stage.”

16The fact that the game is sequential means that it would be impossible to prevent learning acrosselections if subjects completed each election game before proceeding to the next. I solved this problem byimplementing a procedure similar in spirit to the strategy method.

18

Electoral Dynamics

To get a sense for the kinds of promises candidates make and whether moderates or extremists

win elections, Figure 3 presents the sequence of candidate positions and outcomes for selected

sessions (2 one-stage sessions and 2 two-stage sessions). The horizontal axis shows each

election, and the vertical axis shows the promises of the subjects selected as the candidates.

These positions are median-adjusted so that the general election median voter’s position is 0.

The vertical lines show where electoral conditions change in terms of feedback and preference

polarization. General election candidates are depicted using solid shapes (candidates in one-

stage elections and the primary winners in two-stage elections) while primary candidates

who lost the first stage election are depicted with hollow shapes. The winning position of

the general election is shown by the solid line. Although the dynamics of each session differ,

these plots reveal several noteworthy patterns.

First, the positions of candidates from the two parties clearly diverge from the median

voter’s position. This is true for both one-stage and two-stage elections, and it appears to

persist over the course of the experiment even after subjects gain considerable experience.

In session 10 (one stage), for example, the candidates from each party choose positions close

to their own ideal points, and polarization between the candidates’ positions increases when

the underlying preference polarization increases. Along with divergence, there also appears

to be substantial heterogeneity and fluctation in candidate positions.17

Second, while the general election candidate closer to the median voter’s position

generally wins, it is rare for the winning candidate to be located exactly at the predicted

equilibrium position. Even in session 4 (one stage), in which the electoral outcome appears

most frequently near the median voter’s position, the winning candidate is located at the

median’s position in only 3 elections (in another 8 elections, the winning candidate is ±1

from the median voter’s position). In session 10, the winning candidate usually appears to

be just barely closer to the median voter than the losing candidate.

17The figures also reveal that candidates and voters sometimes make mistakes. For example, in election 1in session 4, both parties’ candidates are located to the left of the median voter, with the party R candidatelocated at leftmost position in the policy space. 19

-100-50050100Position

010

2030

40El

ectio

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Righ

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-100-50050100Position

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20

Third, primary voters sometimes select more extreme candidates and sometimes select

more moderate candidates. Notably, there are several candidates in two-stage elections who

locate at exactly the median voter’s position yet lose the primary. In session 1, there were 11

out of 14 such candidates, and in session 6, there were 6 out of 10. While this could suggest

that primary voters prefer extremists, there are also many elections in which the more

moderate candidate wins. For example, in election 11 of session 6, the left party candidate

at −30 defeated the candidate at −45, and the right party candidate at 20 defeated the

candidate located at 50, with the right party candidate (who is closer to the median voter)

winning the general election. Indeed, Figure 3 depicts losing candidates in primary elections

on either side of the parties’ winning candidates (indicated by the fact that the hollow

candidate markers appear both above and below the solid ones).

These sample dynamics suggest that standard game theoretic analysis poorly predicts

candidate positions and voting behavior in the experiment. Whereas equilibrium predicts

complete candidate candidate convergence in both one-stage and two-stage elections, I find

that candidates’ positions diverge. The considerable hetergeneity in candidate positions and

the selection of extreme candidates by primary voters indicate that behavioral game theory

and non-equilibrium analysis may be useful tools for understanding the consequences of

electoral institutions. Of course, Figure 3 only provides a snapshot of experimental behavior.

The remainder of the analysis demonstrates that many of the patterns described above

generalize across subjects and sessions.

Candidate Positions

Figure 4 shows the average positions over time and by election format for all candidates

(top panel) and for winning candidates (bottom panel). In the remainder of the analysis, I

measure the extremity of a candidate’s position (vertical axis) by normalizing positions so

that a subject’s own ideal point is 1 and the median voter’s ideal point is 0 (the opposing

party’s ideal point is −1 on this transformed scale). The top panel of Figure 4 shows that

21

candidate positions clearly diverge from the median voter’s position throughout the exper-

iment regardless of the election format. This divergence also appears to persist over time

and with no apparent effect of primary elections on polarization. The average normalized

position across all rounds is 0.452 in the 1S condition and 0.456 in the 2S conditions. Sub-

jects choose positions only slightly closer to the median voter than the midpoint between

their group’s ideal point and the median voter’s ideal point. While the bottom panel shows

less stability in the positions of winning candidates due to the fact that there are a small

number of sessions per treatment, there are some differences conditional on the availability of

feedback. Without feedback, there is slight convergence of winning candidates to the median

voter’s position in elections without primaries and an increase in divergence once feedback

is introduced in election 11. In elections with primaries, however, the positions of winning

candidates remain polarized throughout the experiment.

Table 1 presents a series of ordinary least squares regressions to measure the effect

of primaries on candidate divergence while controlling for feedback and experience. The

estimates generally reinforce the visual interpretation of the data displayed in Figure 4.

Positions are divergent (as measured by the intercept) and do not change over time (as the

coefficients on Experience are small and insigificant across the models). Although primary

elections have no effect on the positions chosen by all candidates (column 1), they do have

a statistically significant effect on the divergence between party candidates (those standing

for election in the second voting stage, column 2) in the absence of feedback. In 1S elections,

the divergence of party candidates from the median voter is 0.4 on the normalized scale

(i.e., 40% of the distance between the median and the party ideal point) and increases by a

fairly substantial 0.175 in 2S elections (to 57.5% of the distance between median and party

ideal point). The natural consequence of this divergence in party candidates is that election

outcomes are more extreme in 2S elections than in 1S elections (column 3).

The effect of primary elections disappears, however, when feedback is introduced,

as none of the treatment effects in columns (4), (5), or (6) are statistically significant.

22

0.2

.4.6

.81

Mea

n No

rmal

ized

Posit

ions

1 10 20 30 40Election

One Stage Two Stage

All Candidates0

.2.4

.6.8

1M

ean

Norm

alize

d Po

sitio

ns

1 10 20 30 40Election

One Stage Two Stage

Winning Candidates

Figure 4: Average positions and outcomes

23

Table 1: Regression analysis of positions

No feedback (elections 1-10) Feedback (elections 11-40)(1) (2) (3) (4) (5) (6)All Party Winner All Party Winner

Primary (2S) Elections 0.004 0.175* 0.178** 0.003 0.046 0.011(0.060) (0.067) (0.058) (0.042) (0.090) (0.102)

Increased Polarization 0.081 -0.098 0.007 0.016 0.044 0.022(0.041) (0.102) (0.143) (0.022) (0.050) (0.080)

Experience -0.008 0.013 -0.007 -0.000 -0.002 -0.003(0.009) (0.017) (0.023) (0.001) (0.004) (0.004)

Constant 0.387** 0.400** 0.326** 0.469** 0.499** 0.459**(0.058) (0.051) (0.062) (0.042) (0.103) (0.111)

N 1820 260 130 5460 780 390R2 0.001 0.028 0.047 0.0001 0.004 0.004

* p < .05 ** p < .01, OLS regressions with robust standard errors in parentheses, clusteredby subjects in (1), (4) and sessions in (2), (3), (5), and (6).

Comparing the intercepts with and without feedback suggests that this is because candidates

in 1S elections take more extreme positions once feedback is introduced. Indeed, in 1S

elections the average party candidate’s position is 0.407 without feedback and increases to

0.487 in elections with feedback. In 2S elections, feedback appears to have the opposite

effect with average positions starting at 0.581 without feedback and decreasing to 0.532 with

feedback. The effect of primaries on party candidate divergence thus disappears as the result

of countervailing effects of feedback across institutions.18

18The persistence of candidate divergence in a one-dimensional spatial setting is surprising given thatprevious experiments find a consistent tendency for candidates to converge to the median voter’s position(Collier et al. 1987, McKelvey and Ordeshook 1985, Morton 1993) or for outcomes to converge to theCondorcet winner (Fiorina and Plott 1978, McKelvey and Ordeshook 1982, Palfrey 2006). The difference mayhave to do with the fact that candidates are policy-motivated in my experiment rather than office-motivatedin most previous experiments, but there are a number of other subtle differences between my design andprevious experiments, including the use of linear instead of quadratic utility, random role assignment, thestrategy method, and the varying of the numerical value of players’ ideal points. Isolating the exact cause ofthe difference would be interesting, but is largely beyond the scope of this paper. Nevertheless, I conducteda modified version of the experiment (discussed in the Appendix) in which I increase the salience of players’decisions by assigning fixed roles. The main result that candidates diverge in both 1S and 2S elections holdsup in the modified Fixed Roles Experiment. Some differences emerge, including movement towards themedian over the course of the experiment and greater polarization in 2S than in 1S, though the magnitude

24

Looking only at average positions obscures the effects of primary elections on other

aspects of the distribution of candidate positions. Although the effect of primaries on average

positions is limited to elections without feedback, I find that primaries cause candidate

positions to become more tightly centered around the mean—that is, less dispersed. Figure

5 plots the standard deviation of candidate and winning positions over the course of the

experiment. The graphs reveal two interesting patterns in candidate dispersion. First,

we see dispersion decreasing steadily over time. Thus, because average positions remain

unchanged, positions converge not to the median voter’s position, but to the mean position

in both 1S and 2S elections. Second, we observe a clear effect of primary elections on

dispersion. Variation in candidate positions and in the positions of winning candidates is

consistently lower in 2S elections than in 1S elections (compare standard deviations of 0.47

in the former and 0.55 in the latter, with the difference statistically signficant according to

a variance ratio test, p < 0.01). Primary elections therefore appear to reinforce candidate

polarization.

Voting Behavior

The sample dynamics and analysis of candidate positions suggest that, rather than causing or

exacerbating polarization, primaries instead help to maintain polarization by playing a role

in the selection of candidates, weeding out party candidates who are either too extreme or

too moderate. In this section, I examine voting behavior in primaries by assessing the extent

to which primary voters prefer moderates or extremists and by determining the behavioral

rule that best fits the experimental data.

Voters tend to select the more extreme candidate, but it is not an overwhelming

preference. Overall, voters prefer the extremist in 57% of the elections in the data. When

the moderate candidate’s position is closest to the median voter (between 0 and 0.2 on the

normalized scale), voters overwhemingly choose the extremist (69%), especially when both

of the effect is modest.

25

0.2

.4.6

.81

St. D

ev. N

orm

alize

d Po

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1 10 20 30 40Election

One Stage Two Stage

All Candidates0

.2.4

.6.8

1St

. Dev

. Nor

mal

ized

Posit

ions

1 10 20 30 40Election

One Stage Two Stage

Winning Candidates

Figure 5: Disperson of positions and outcomes

26

candidates are close to the median voter (90%). Yet, there is an asymmetry because when

the extremist candidate’s position is extreme (closest to its own ideal point between 0.8 and

1 on the normalized scale), the choice between the moderate and extremist is essentially a

coin flip (extremist wins 51% of the time). The more moderate candidates do best when

they locate near the midpoint between their party’s ideal point and the median voter and

when the extremist is more extreme, but even then, the moderate does not do much better

than a coin flip, winning elections at most 57% of the time (when the moderate is between

0.4 and 0.6 and the extremist is between 0.6 and 0.8).19

In Table 2, I characterize voting in each group of 10 elections according to three

possible behavioral rules. The first row shows the percentage of votes for the moderate

candidate. Notice that fewer than half of votes cast favor the moderate candidate, 37%

in the first 10 elections without feedback, increasing slightly to 44 − 46% in elections with

feedback. The slight increase in voting for moderates appears to lend some support for the

theoretical framework, as the change in positioning behavior when feedback is introduced is

consistent with the change in voting behavior. Without feedback, more votes are cast for

extremists than moderates (63% versus 37%); if candidates expected this, then their best

responses would have been to take more extreme positions, which is consistent with the effect

of primaries in elections 1-10. When feedback is introduced, there is an uptick in voting for

moderate candidates, which would lead candidates to expect less extreme opponents and

hence to moderate their own behavior.

However, primary voters do not express clear, unconditional preferences for either

moderate or extremist party candidates. Table 2 therefore characterizes two additional

behavioral rules. The second row shows that a simple “midpoint” strategy where voters

select the candidate closest to the midpoint between the median voter and their party’s

position is a better description of behavior than voting for the moderate (or the extremist).

19See the Appendix for additional details about voting behavior as a function of the candidates’ positions.

27

Table 2: Primary voting behavior

ElectionsVoting rule 1-10 11-20 21-30 31-40 Total

Closer to median voter 37% 44% 46% 46% 43%(525) (575) (630) (635) (2,365)

Closer to midpoint 67% 65% 64% 65% 65%(645) (640) (680) (655) (2,620)

Closer to own promise 45% 76% 75% 78% 68%(648) (644) (671) (652) (2,615)

Roughly two-thirds of votes (overall 65%) are consistent with this rule (compared to the 43%

consistent with voting for moderates and 57% voting for extremists).

The third row of Table 2 presents analysis of the third voting rule in which voters

behave as if they have heterogeneous “belief-induced ideal points.” This rule appears to

be the most consistent with the data. It assumes that each voter has an individual belief

that a candidate located at v∗i maximizes their expected utility and therefore votes for the

candidate closest to v∗i . In the experiment, subjects effectively express such belief-induced

ideal points when they choose campaign promises at the beginning of each election, so I use

a subject’s campaign promise as a measure of their belief-induced ideal point. This voting

rule attains the highest rate of classification success, outperforming the simple midpoint

rule in elections with feedback. By elections 31-40, 78% of votes are consistent with voting

for the candidate closest to the belief-induced ideal point (one’s own promise earlier in the

election), compared to 46% for moderates, 54% for extremists, and 65% for the midpoint

strategy. Because campaign promises and belief-induced ideal points diverge from the median

voter’s position, this voting rule has the effect of reducing variance in candidate positions

and reinforcing candidate polarization (as discussed in the theoretical analysis and consistent

with the patterns shown in Figure 5).

28

A Direct Test of Beliefs and Behavior

The experimental findings that candidate positions diverge from the median voter’s position

in both 1S and 2S elections supports the behavioral theory predicated on out-of-equilibrium

beliefs (Prediction 3) over the competing predictions based on fully strategic candidate be-

havior (Predicitons 1 and 2). This inference is indirect, however, because beliefs are neither

measured nor manipulated in the experiment. To generate a more direct test of the connec-

tion between beliefs and behavior, I conducted another version of the experiment in which

beliefs are more carefully controlled and manipulated. In this version of the experiment,

subjects play candidates in the 2S election game. Greater control over beliefs is achieved by

having subjects play against computer opponents rather than other subjects. This ensures

that the distribution of positions is known and exogenous. Variation in beliefs is induced by

providing truthful information about whether the opposing party’s candidate is moderate or

extreme.

I conducted three sessions of the modified experiment (54 participants, 18 subjects

per session). Each subject played 20 rounds of the 2S game (with feedback) against computer

opponents.20 The game is modified so that subjects know that the opposing candidate’s posi-

tion in the general (second stage) election is stochastically determined by a two-part process.

First, two opposing primary candidates’ positions are randomly drawn from a uniform dis-

tribution over the positions between the median voter’s ideal point and the opposing party’s

ideal point. Second, the opposing party’s primary voter (also the computer) randomly selects

one of the two positions with equal probability. Information about whether the opposing

computer voter chose the moderate or extremist is then provided to the subject. The con-

20The sessions were divided into three parts, with the candidate choices of interest coming in Part 3. Theprocedures for Part 1 are the same as in the main experiment for the 2S election game without feedback.This ensures that subjects have the same experience with the game as the subjects in the original experiment.The only minor differences are that groups have 9 players instead of 7 and the distance between parties isheld constant at 120. Part 2 involves voting against random opponents, but those data are not analyzedhere.

29

01

23

Dens

ity

0 .25 .5 .75 1Normalized Promise

Moderate Opponents Extremist Opponents

Figure 6: Candidate positions against random (computer-selected) moderates and extremists

sequence of this two-part procedure is that candidates will face one of the right-triangular

distributions shown in the top-right and bottom-right of Figure 2. When the opponent is

known to be more moderate, the distribution skews towards the median voter, and when the

opponent is known to be more extreme, the distribution skews toward the opposing party’s

ideal point.

Figure 6 provides a comparison of the distributions, plotted as kernel densities, that

candidates take against moderates versus extremists. The results demonstrate that subjects

clearly respond to information about the extremity of their opponents. When comput-

ers select moderate opponents, human candidates take correspondingly moderate positions.

Specifically, the majority of positions (69%) fall between 0 and 0.25 on the normalized scale

(25% of the distance from the median to their own party’s ideal point). When opponents

are extreme, the distribution of positions shifts considerably towards their own party’s ideal

point (67% of the distribution shifts to above 0.25). In addition, the mode increases sharply,

from within the interval between 0 and 0.25 to 0.5 on the normalized scale. The mean po-

sition shifts from 0.20 against moderates to 0.35 against extremists, and this difference is

30

statistically significant (p < 0.01). These results provide direct evidence that candidates’ po-

sitions respond to exogenously induced changes in their beliefs, supporting the belief-based

behavioral theory.

Conclusion

Analytically, I strip away many of the complexities of real-world elections and focus on how

introducing voters affects candidate positions in a stark environment with policy-motivated

actors and complete information. When candidates and voters have imperfect, out-of-

equilibrium beliefs about the behavior of their opponents, the extremity of the positions

and candidates they choose depends on how extreme they expect their opponents to be.

Thus, the effect of primary elections is conditioned by beliefs and strategic expectations.

Experimentally, I find that the need to win a partisan primary does not affect can-

didates’ positions. To the extent there is any polarization, it occurs because primary voters

select extremists more often than they select moderates—that is, through the behavior of

voters rather than the strategic responses of candidates. The effect is relatively small and

limited to settings in which participants cannot learn about the behavior of others from past

experience.

Interestingly, the experimental data also demonstrate that primary elections may in

fact contribute to “ideological purity,” but not in the way that conventional wisdom suggests.

Primary voters do not seem to care about ideological purity per se. Instead, voters appear

to be sophisticated enough to use the primary process to weed out candidates both too close

and too far from the general election median voter’s position. Thus, voters in the lab seem

to recognize the tension between centrist policies that yield few policy benefits and extreme

positions that are unlikely to win the general election, resolving the trade-off by generally

splitting the difference. Candidates are responsive to this selective weeding out by voters and,

as a consequence, take positions that are more homogeneous in elections with primaries than

31

elections without them. Moreover, candidates are responsive to exogenous manipulations of

opposing candidates’ positions, which provides direct support for the mechanism posited by

the theory.

The behavioral theory helps to make sense of the fact that many people blame partisan

primary elections for much of the polarization and dysfunction that afflicts the contemporary

American political system but empirical research has not been able to provide compelling

evidence to support the claim. For example, the theory is consistent with the findings that

neither the introduction of direct primaries (Hirano et al. 2010) nor the format of primary

elections (McGhee et al. 2014) has much to do with increasing polarization. It is also

consistent with the fact that polarization has been increasing over time despite the absence

of significant changes in electoral institutions.

A direction for future observational research would be to explore the notion that

strategic expectations about increasing polarization may, to some extent, be self-fulfilling.

For example, the theory implies that partisans who increasingly perceive the opposing party’s

candidates to be more extreme will be emboldened to support more extreme candidates of

their own (e.g., this may explain Bernie Sanders’ popularity in the 2016 Democratic primary).

With appropriate measures, this hypothesis could be tested both cross-sectionally or over

time, and it is entirely plausible to the extent that citizens infer extreme ideological positions

from their dislike of the opposing party (Brady and Sniderman 1985) given the steady rise

of negative partisanship and affective polarization (Abramowitz and Webster 2016, Iyengar,

Sood and Lelkes 2012).

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Online Appendix

Table A3 provides a more detailed description of voting behavior as a function of the can-didates’ positions than is described in the main text of the paper. Each cell shows thepercentage of votes cast for the moderate candidate (the candidate closer to the medianvoter) for a given range of candidate positions.

Table A3: Votes for moderate by candidates’ positions

Extremist’s Position

[0, .2) [.2, .4) [.4, .6) [.6, .8) [.8, 1] Total

[0, .2) 10% 23% 27% 36% 41% 31%(10) (115) (165) (135) (100) (525)

[.2, .4) 36% 43% 48% 53% 45%(100) (195) (185) (95) (575)

Moderate’s [.4, .6) 47% 57% 50% 53%Position (85) (190) (145) (420)

[.6, .8) 55% 55% 55%(20) (110) (130)

[.8, 1] 40% 40%(30) (30)

Total 10% 29% 38% 48% 49% 43%(10) (215) (445) (530) 480 1,680

Fixed Roles Experiment

Procedures

I designed and conducted a different version of the experiment in an effort to increase thesalience of the candidate positioning decisions and to create an experimental environmentthat more closely matches the theoretical analysis of best responses to out-of-equilibriumbeliefs. Increased salience was achieved primarily by assigning subjects to fixed roles. Insteadof choosing positions in each round before candidates are selected (as the main experiment),subjects are randomly assigned to roles as candidates and voters before the first election

38

and then retain their roles throughout the experiment. In the 1S condition of the fixedrole experiment, all subjects are candidates and are randomly matched in pairs for eachelection (one left candidate against one right candidate, with no subjects as voters). In the2S condition, groups of 3 (two candidates and one voter) are matched against each other,so each play of the game involves 6 subjects. There are 30 elections in Part 1, all withfeedback, so Part 1 of fixed role experiment is a close analogue to Part 2 of main experiment(the 30 elections with feedback). I conducted two sessions of the fixed role experiment with1S elections (36 subjects) and three sessions with 2S elections (48 subjects) at the *******.

Elections 31-50 of the fixed role experiment are designed to elicit candidates’ choicesin an experimental setting closer to the theoretical analysis of best responses to out-of-equilibrium beliefs. Rather than allowing beliefs about opposing candidates to arise endoge-nously as uncontrolled, subjective beliefs, I rely on experimental control over the distributionof candidates. More specifically, in Part 2 of the 1S condition, opposing candidates’ posi-tions are not chosen by another human subject but are instead drawn randomly from auniform distribution (over the positions between the median voter’s ideal point and the op-posing party’s ideal point). Thus, I achieve control over the beliefs about the distribution ofopposing candidates by controlling the positions of the opposing candidates themselves.

The procedure in the 2S condition is somewhat different to allow human voters toselect candidates within each primary. The aim was to create a setup in which the initialdistribution of candidates within each party is identical to the 1S election but where thedistribution of the candidates in the general election depends on the behavior of primaryvoters. This setup closely matches the theoretical analysis while at the same time allowingthe effect of primaries to arise endogenously from subjects’ behavior. However, this setupdoes not manipulate beliefs or information directly the way that the direct test does in themain text of the paper. In elections 31-40, all subjects act as voters and are paired againstone voter from the other party. The voters simultaneously choose between two randomcandidates from a uniform distribution on their own side of the policy space, and the outcomeof each election is the candidate closest to the median voter’s position. In elections 41-50, allsubjects then act as candidates and face an opposing (computer) candidate with a positiondrawn randomly from the results of the previous set of elections (31-40). This design allowsvoting behavior to arise endogenously (in elections 31-40) and then holds it constant insubsequent elections (41-50) to preclude changes in voting behavior that might result fromstrategic interaction with candidates; this setup also removes any potential for intra-partycompetition and renders beliefs about opposing primary voters’ behavior as the only factorrelevant to the positioning decision.

Results

Figure A1 shows the average positions over time in the fixed roles experiment, plotted sep-arately for 1S and 2S elections. In contrast to the original setup, primaries with fixed rolescause candidates to take more extreme positions than they do in 1S elections. The toppanel of Figure A1 suggests that this effect is modest but persistent over time. Similar tothe original experiment, I find that positions consistently diverge from the median voter’sposition in all 30 elections regardless of the election format. In the first five rounds, theaverage normalized position in 1S elections is .376 compared to .531 in 2S elections. In

39

Table A4: Regression analysis of positions in the Fixed Roles Experiment

(1) (2) (3)

All Party Winner

Primary (2S) Elections 0.088** 0.056** 0.057**

(0.015) (0.017) (0.016)

Experience -0.006** -0.006** -0.004**

(0.001) (0.001) (0.001)

Constant 0.417** 0.415** 0.253**

(0.016) (0.016) (0.015)

Observations 2040 1560 780

R2 0.0391 0.0338 0.0400

* < .05 ** < .01

the last five rounds, the average in 1S elections diminishes to .251 compare to .353 in 2Selections. The regression analyis in Table A4 provides more precise estimates of the effectof primaries while controlling for experience. Primary elections have a significant effect onthe divergence of all candidates’ positions from the median voter (column 1), which thentranslates to a greater divergence in party candidates’ positions (column 2), and electionoutcomes (column 3). Every candidate decision is consequential, yet increasing the salienceof candidates’ decisions is not sufficient to generate full convergence to the median voter’sideal point even though candidates’ positions gradually become more moderate over time.

Turning now to the elections against random opponents’ positions, I find that behavioragainst random candidate positions is no different than behavior against human players.In 1S elections, the mean normalized position is .329 against human candidates and .328against randomly drawn positions. In 2S elections, the difference in candidate positionsis statistically signficant when all rounds are compared (.417 against humans versus .359against random positions, p < .01), but this difference disappears when accounting forlearning by using only the last 10 elections against human players for the comparison (.344against humans versus .359 against random positions, p = .53). In addition, there is nodifference in strategic voting when selecting between random positions and positions chosenby human players, though the overall rate of voting for moderate candidates is higher in thefixed roles experiment than it was in the original (64% of votes are for moderates againsthuman players and 66% are for moderates against random positions, p = .59). These resultssuggest that candidates in the fixed roles experiment are primarily level-1, choosing positions

40

0.2

.4.6

.81

Norm

alize

d Po

sitio

ns

1 5 10 15 20 25 30Election

One Stage Two Stage

All Positions0

.2.4

.6.8

1No

rmal

ized

Posit

ions

1 5 10 15 20 25 30Election

One Stage Two Stage

Winning Positions

Figure A1: Average positions and outcomes in the Fixed Roles Experiment

41

as if their opponents choose their positions randomly (level-0), providing some additionalsupport for the behavioral theory.

42

Online  Appendix:  Instructions  for  Two-­‐Stage  Elections  (with  Fixed  Matching)  

 Instructions    

 General  Information    This  is  an  experiment  on  the  economics  of  elections.  The  *******  provided  funds  for  this  research.      You  will  be  paid  in  cash  for  your  participation,  and  the  exact  amount  you  receive  will  be  determined  during  the  experiment  and  will  depend  partly  on  your  decisions,  partly  on  the  decisions  of  others,  and  partly  on  chance.  You  will  be  paid  your  earnings  privately,  meaning  that  no  other  participant  will  find  out  how  much  you  earn.  These  earnings  will  be  paid  to  you  at  the  end  of  the  experiment  along  with  the  $7  participation  payment.    Pay  attention  and  follow  the  instructions  closely,  as  we  will  explain  how  you  will  earn  money  and  how  your  earnings  will  depend  on  the  choices  that  you  make.  Each  participant  has  a  printed  copy  of  these  instructions,  and  you  may  refer  to  them  at  any  time.    If  you  have  any  questions  during  the  experiment,  please  raise  your  hand  and  wait  for  an  experimenter  to  come  to  you.  Please  do  not  talk,  exclaim,  or  try  to  communicate  with  other  participants  during  the  experiment.  Also,  please  ensure  that  any  phones  or  electronic  devices  are  turned  off  and  put  away.  Participants  intentionally  violating  the  rules  will  be  asked  to  leave  and  may  not  be  paid.      Parts  and  Elections    This  experiment  consists  of  several  parts.  Each  part  consists  of  a  series  of  elections,  and  we  will  explain  the  instructions  for  each  part  before  beginning  that  part.      We  will  randomly  select  one  election  to  count  for  payment  from  the  entire  session.  Each  election  is  equally  likely  to  be  selected.  The  points  you  receive  from  that  election  will  be  used  to  calculate  your  payment  for  the  experiment,  and  points  will  be  converted  to  cash  at  the  rate  of  $1  for  every  10  points.  You  should  think  of  each  election  as  a  separate  decision  task.    Before  we  begin,  we  will  randomly  divide  you  into  two  groups  of  seven  participants.  This  random  assignment  will  take  place  once  so  that  the  members  of  your  group  will  be  the  same  in  every  round.    

Online  Appendix:  Instructions  for  Two-­‐Stage  Elections  (with  Fixed  Matching)  

Part  1    There  will  be  10  elections  in  Part  1,  and  each  election  consists  of  three  stages:  a  campaign  stage  and  two  voting  stages.    Campaign  Stage    In  the  campaign  stage,  you  will  choose  a  whole  number  from  1  to  200.  This  number  is  your  “campaign  promise”  and  you  can  think  of  it  as  a  position  or  stance  on  a  particular  policy  issue  that  both  voters  and  candidates  care  about.  If  you  are  selected  as  a  candidate  and  you  win  the  election,  then  this  number  will  determine  the  payoffs  for  each  voter  and  candidate  (as  we  will  explain  later).    Once  all  of  the  participants  have  chosen  a  campaign  promise,  the  computer  will  then  select  two  members  of  each  group  at  random  to  be  candidates  (all  members  of  the  group  are  equally  likely  to  be  selected),  and  then  we  will  move  to  the  voting  stages.  Note  that  even  though  only  two  members  of  your  group  will  be  selected  as  candidates,  you  should  choose  your  campaign  message  as  if  you  were  actually  selected  as  a  candidate.    First  Voting  Stage    The  members  of  each  group  who  are  not  selected  as  candidates  will  be  the  voters.  Thus,  in  each  group  there  will  be  2  candidates  and  5  voters.      In  the  first  voting  stage,  each  group  votes  to  determine  which  of  the  group’s  two  candidates  will  be  a  candidate  in  the  second  voting  stage.  The  candidate  who  receives  the  most  votes  will  move  on  to  the  second  voting  stage.  Only  members  of  your  group  will  be  voting  on  the  candidates  from  your  group  in  the  first  voting  stage.  The  other  group  will  be  voting  on  their  own  two  candidates  at  the  same  time.      Second  Voting  Stage    The  winners  of  each  group’s  first  vote  will  then  be  the  two  candidates  in  the  second  voting  stage.  That  is,  there  is  one  candidate  from  each  group  in  the  second  stage.  All  voters  from  both  groups  will  vote  in  the  second  stage.  The  candidate  who  receives  the  most  votes  wins  the  election.  In  addition,  there  will  be  one  “computer  voter”  in  the  second  stage  of  voting.  The  computer  voter  is  not  a  member  of  either  group  but  is  like  a  robot  programmed  to  always  vote  for  the  candidate  whose  campaign  promise  gives  it  the  higher  payoff  value  (the  promise  closest  to  its  own  favorite  position,  as  described  below).  If  both  candidates  in  the  second  stage  offer  the  computer  voter  the  same  payoff,  then  the  computer  voter  will  cast  its  vote  randomly  between  the  two  candidates  (with  votes  for  each  candidate  equally  likely).            

Online  Appendix:  Instructions  for  Two-­‐Stage  Elections  (with  Fixed  Matching)  

Payoffs    In  each  round,  you  will  be  assigned  a  “favorite  position”  and  you  will  earn  points  based  on  how  close  the  winning  candidate’s  campaign  promise  is  to  your  favorite  position.      The  closer  the  winning  campaign  promise  is  to  your  favorite  position,  the  more  points  you  will  earn.  Specifically,  we  will  compute  the  absolute  difference  between  the  winning  campaign  promise  and  your  favorite  position  and  then  subtract  this  amount  from  200.  This  is  described  by  the  following  formula:    

Points  =  200  -­‐  |Winning  campaign  promise  –  Your  favorite  position|    

For  example,  if  your  favorite  position  is  57  and  the  campaign  promise  of  the  candidate  who  wins  the  second  election  is  27,  then  your  points  from  that  election  are  200  -­‐  |57  –  27|  =  200  –  30  =  170  points.  Of  course,  this  is  just  one  example.  Note  also  that  candidates  and  voters  (including  the  computer  voter)  all  earn  points  according  to  the  same  formula;  candidates  do  not  earn  extra  points  for  winning.  Remember  that  we  will  pay  you  $1  for  every  10  points  you  earn  (rounded  to  the  nearest  quarter).    In  every  election,  each  group  will  have  a  different  favorite  position.  Within  groups,  every  member’s  favorite  position  will  be  the  same.  For  example,  if  your  group’s  favorite  position  is  50  and  the  other  group’s  favorite  position  is  150,  then  everyone  in  your  group  has  a  favorite  position  of  50  while  everyone  in  the  other  group  has  a  favorite  position  of  150.  The  computer  voter  will  always  have  a  position  that  is  somewhere  between  the  two  groups.  Everyone  will  find  out  the  values  of  these  favorite  positions  at  the  beginning  of  each  election.      Sequence  of  Decisions    In  Part  1  you  will  make  your  decisions  for  all  of  the  elections  in  each  stage  separately  before  moving  on  to  the  next  stage.  In  other  words,  first  you  will  choose  your  campaign  promises  for  all  elections  before  moving  to  the  voting  stages.  Second,  you  will  cast  your  votes  in  all  first  voting  stages  for  which  you  are  a  voter.  Finally,  you  will  cast  your  votes  in  all  second  voting  stages  for  which  you  are  a  voter.  Note  that  you  will  not  receive  any  feedback  about  results  of  the  elections  from  Part  1.      Summary    

 1. Before  any  of  the  elections,  you  are  randomly  divided  into  two  groups.  These  groups  

will  remain  the  same  throughout  the  experiment.    

2. In  every  round,  you  will  find  out  the  favorite  position  of  your  group,  the  other  group,  and  the  computer  voter.    

Online  Appendix:  Instructions  for  Two-­‐Stage  Elections  (with  Fixed  Matching)  

3. In  the  campaign  stage,  you  choose  a  number  from  1-­‐200  that  serves  as  your  campaign  promise.  If  you  are  elected,  this  campaign  promise  determines  everyone’s  payoff.  

 4. We  randomly  determine  two  members  of  each  group  to  be  candidates  and  the  other  

members  to  be  voters.    5. In  the  first  voting  stage,  each  group  simultaneously  selects  which  of  its  candidates  to  

put  forward  in  the  second  voting  stage.      6. In  the  second  voting  stage,  there  is  one  candidate  from  each  group.  In  addition,  there  is  

a  computer  voter  that  will  vote  for  the  candidate  whose  campaign  promise  is  closest  to  its  own  favorite  position.  The  campaign  promise  of  the  candidate  who  wins  the  second  voting  stage  determines  everyone’s  payoff  for  that  election.  

 7. Your  payoff  is:      

Points  =  200  -­‐  |Winning  campaign  promise  –  Your  favorite  position|    

The  closer  the  winning  campaign  promise  is  to  your  favorite  position,  the  more  points  you  will  earn.    

   Are  there  any  questions?  If  you  have  a  question,  please  raise  your  hand.      Instructions  Quiz    Before  we  begin  the  experiment  we  would  like  you  to  answer  a  few  questions  to  make  sure  you  understand  how  election  experiment  works.  You  will  answer  these  questions  on  your  computers  and  will  receive  immediate  feedback  once  you  answer  all  of  the  questions.  We  will  then  begin  the  experiment  when  everyone  has  answered  these  questions.    

1. If  your  favorite  position  is  20  and  the  winning  candidate’s  campaign  promise  is  90,  how  many  points  would  you  earn?    

2. If  your  favorite  position  is  165,  your  campaign  promise  is  150,  and  you  win  the  election,  how  many  points  would  you  earn?  

 3. Suppose  that  the  results  of  the  first  stage  votes  are  as  follows.  In  Group  L,  Candidate  

A  receives  3  votes  and  Candidate  B  receives  2  votes.  In  Group  R,  Candidate  C  receives  1  vote  and  Candidate  D  receives  4  votes.  Which  candidates  will  you  be  able  to  vote  for  in  the  second  stage  vote?    

4. Suppose  that  the  computer  voter’s  favorite  position  is  80.  If  Candidate  A’s  campaign  promise  is  50  and  Candidate  B’s  campaign  promise  is  120,  which  candidate  would  the  computer  vote  for?    

Online  Appendix:  Instructions  for  Two-­‐Stage  Elections  (with  Fixed  Matching)  

Part  2    There  are  30  elections  in  Part  2.  The  rules  for  elections  in  Part  2  are  exactly  the  same  as  in  Part  1.  Each  election  will  consist  of  a  campaign  stage  and  two  voting  stages.  The  payoffs  will  also  be  determined  in  the  same  way  as  before.      In  Part  2  only  the  sequence  of  decisions  and  the  feedback  you  receive  about  decisions  will  be  different.  Instead  of  making  all  of  your  decisions  for  each  stage  before  moving  to  the  next  stage,  you  will  make  your  decisions  in  sequence  for  each  election  separately.  In  other  words,  for  the  first  election,  you  will  choose  your  campaign  promise,  then  cast  your  first  stage  vote,  and  then  cast  your  second  stage  vote.  After  the  second  stage  vote  you  will  learn  the  results  of  the  election  immediately  after  the  election  is  finished.  You  will  then  move  on  to  the  next  election,  beginning  with  the  campaign  promise  stage,  and  so  on.    Are  there  any  questions?  If  you  have  a  question,  please  raise  your  hand.    

Online  Appendix:  Instructions  for  Direct  Test  of  Belief  Manipulation  

 Instructions  

 General  Information    This  is  an  experiment  on  the  economics  of  elections.  The  **********  has  provided  the  funds  for  this  research.      You  will  be  paid  in  cash  for  your  participation,  and  the  exact  amount  you  receive  will  be  determined  during  the  experiment  and  will  depend  partly  on  your  decisions,  partly  on  the  decisions  of  others,  and  partly  on  chance.  You  will  be  paid  your  earnings  privately,  meaning  that  no  other  participant  will  find  out  how  much  you  earn.  These  earnings  will  be  paid  to  you  at  the  end  of  the  experiment  along  with  the  $7  participation  payment.    Pay  attention  and  follow  the  instructions  closely,  as  we  will  explain  how  you  will  earn  money  and  how  your  earnings  will  depend  on  the  choices  that  you  make.  Each  participant  has  a  printed  copy  of  these  instructions,  and  you  may  refer  to  them  at  any  time.    If  you  have  any  questions  during  the  experiment,  please  raise  your  hand  and  wait  for  an  experimenter  to  come  to  you.  Please  do  not  talk,  exclaim,  or  try  to  communicate  with  other  participants  during  the  experiment.  Also,  please  ensure  that  any  phones  or  electronic  devices  are  turned  off  and  put  away.  Participants  intentionally  violating  the  rules  will  be  asked  to  leave  and  may  not  be  paid.      Parts  and  Elections    This  experiment  consists  of  several  parts.  Each  part  consists  of  a  series  of  elections,  and  we  will  explain  the  instructions  for  each  part  before  beginning  that  part.      We  will  randomly  select  one  election  to  count  for  payment  from  the  entire  session.  Each  election  is  equally  likely  to  be  selected.  The  points  you  receive  from  that  election  will  be  used  to  calculate  your  payment  for  the  experiment,  and  points  will  be  converted  to  cash  at  the  rate  of  $1  for  every  10  points.  More  specifically,  we  will  take  the  total  number  of  points  you  earned  in  the  election  that  counts,  divide  by  10,  and  then  round  this  amount  to  the  nearest  quarter.  You  should  think  of  each  election  as  a  separate  decision  task.        

Online  Appendix:  Instructions  for  Direct  Test  of  Belief  Manipulation  

Part  1    There  will  be  10  elections  in  Part  1,  and  each  election  consists  of  three  stages:  a  campaign  stage  and  two  voting  stages.    Campaign  Stage    In  the  campaign  stage,  you  will  choose  a  whole  number  from  1  to  200.  This  number  is  your  “campaign  promise”  and  you  can  think  of  it  as  a  position  or  stance  on  a  particular  policy  issue  that  both  voters  and  candidates  care  about.  If  your  position  is  selected  as  the  winner  of  the  election,  then  this  number  will  determine  the  payoffs  for  each  participant  (as  we  will  explain  later).    Once  all  of  the  participants  have  chosen  their  campaign  promises,  the  computer  will  then  randomly  select  two  promises  from  each  group  (with  each  member’s  promise  equally  likely  to  be  selected),  and  then  we  will  move  to  the  voting  stages.  Note  that  even  though  only  two  promises  from  your  group  will  be  selected,  you  should  choose  your  campaign  promise  as  if  it  were  actually  selected.    First  Voting  Stage    In  the  first  voting  stage,  each  group  votes  to  select  one  of  the  group’s  two  promises  to  put  forward  for  the  second  voting  stage.  The  promise  that  receives  the  most  votes  will  move  on  to  the  second  voting  stage.  If  the  vote  is  a  tie,  each  promise  is  equally  likely  to  be  selected.  Only  members  of  your  group  will  be  voting  on  the  promises  from  your  own  group  in  the  first  voting  stage.  The  other  group  will  be  voting  on  their  own  two  promises  at  the  same  time.      Second  Voting  Stage    In  the  second  voting  stage,  a  “computer  voter”  chooses  the  winning  promise  from  the  promises  put  forward  by  the  groups.  The  computer  voter  is  not  a  member  of  either  group  but  is  like  a  robot  programmed  to  always  vote  for  the  candidate  whose  campaign  promise  gives  it  the  higher  payoff  value  (the  promise  closest  to  its  own  favorite  position,  as  described  below).  If  both  promises  in  the  second  stage  offer  the  computer  voter  the  same  payoff,  then  the  computer  voter  will  cast  its  vote  randomly  between  the  two  promises  (with  each  promise  being  equally  likely  to  win).    Payoffs    In  each  round,  you  will  be  assigned  a  “favorite  position”  and  you  will  earn  points  based  on  how  close  the  winning  candidate’s  campaign  promise  is  to  your  favorite  position.      The  closer  the  winning  campaign  promise  is  to  your  favorite  position,  the  more  points  you  will  earn.  Specifically,  we  will  compute  the  absolute  difference  between  the  winning  

Online  Appendix:  Instructions  for  Direct  Test  of  Belief  Manipulation  

campaign  promise  and  your  favorite  position  and  then  subtract  this  amount  from  200.  This  is  described  by  the  following  formula:    

Points  =  200  -­‐  |Winning  campaign  promise  –  Your  favorite  position|    

For  example,  if  your  favorite  position  is  57  and  the  campaign  promise  selected  by  the  computer  voter  in  the  second  stage  is  27,  then  your  points  from  that  election  are  200  -­‐  |57  –  27|  =  200  –  30  =  170  points.  Of  course,  this  is  just  one  example.  Note  also  that  players  (including  the  computer  voter)  all  earn  points  according  to  the  same  formula.  That  is,  only  the  numerical  value  of  the  promise  matters—you  do  not  earn  extra  points  if  your  promise  is  selected.  Remember  that  we  will  pay  you  $1  for  every  10  points  you  earn  (rounded  to  the  nearest  quarter).    In  every  election,  each  group  will  have  a  different  favorite  position.  Within  groups,  every  member’s  favorite  position  will  be  the  same.  For  example,  if  your  group’s  favorite  position  is  50  and  the  other  group’s  favorite  position  is  150,  then  everyone  in  your  group  has  a  favorite  position  of  50  while  everyone  in  the  other  group  has  a  favorite  position  of  150.  The  computer  voter  will  always  have  a  position  that  is  somewhere  between  the  two  groups.  Everyone  will  find  out  the  values  of  these  favorite  positions  at  the  beginning  of  each  election.      Sequence  of  Decisions    In  Part  1  you  will  make  your  decisions  for  all  of  the  elections  in  each  stage  separately  before  moving  on  to  the  next  stage.  In  other  words,  first  you  will  choose  your  campaign  promises  for  all  elections  before  moving  to  the  voting  stage,  and  then  you  will  cast  your  votes  in  all  of  the  first  voting  stages.  Note  that  you  will  not  receive  any  feedback  about  the  results  of  the  elections  from  Part  1.    Summary    1. Before  any  of  the  elections,  you  are  randomly  divided  into  two  groups.  These  groups  

will  remain  the  same  throughout  Part  1  of  the  experiment.    

2. Before  every  election,  you  will  find  out  the  favorite  position  of  your  group,  the  other  group,  and  the  computer  voter.    

3. In  the  campaign  stage,  you  choose  a  number  from  1  to  200  that  serves  as  your  campaign  promise.  If  your  promise  wins  the  election,  this  campaign  promise  determines  everyone’s  payoff.  

 4. We  randomly  select  two  promises  from  each  group  to  be  the  choices  in  the  first  voting  

stage.    5. In  the  first  voting  stage,  each  group  simultaneously  votes  for  one  promise  to  put  

forward  in  the  second  voting  stage.    

Online  Appendix:  Instructions  for  Direct  Test  of  Belief  Manipulation  

 6. In  the  second  voting  stage,  there  is  one  promise  from  each  group.  The  computer  voter  

will  vote  for  the  campaign  promise  closest  to  its  own  favorite  position.  The  campaign  promise  of  the  group  that  wins  the  second  voting  stage  determines  everyone’s  payoff  for  that  election.  

 7. Your  payoff  is:      

Points  =  200  -­‐  |Winning  campaign  promise  –  Your  favorite  position|    

The  closer  the  winning  campaign  promise  is  to  your  favorite  position,  the  more  points  you  will  earn.    

   Are  there  any  questions?  If  you  have  a  question,  please  raise  your  hand.      Instructions  Quiz    Before  we  begin  the  experiment  we  would  like  you  to  answer  a  few  questions  to  make  sure  you  understand  how  election  experiment  works.  You  will  answer  these  questions  on  your  computers  and  will  receive  immediate  feedback  once  you  answer  all  of  the  questions.  We  will  then  begin  the  experiment  when  everyone  has  answered  these  questions.    

1. If  your  favorite  position  is  100  and  the  winning  campaign  promise  is  140,  how  many  points  would  you  earn?    

2. If  your  favorite  position  is  20  and  the  winning  campaign  promise  is  90,  how  many  points  would  you  earn?    

3. If  your  favorite  position  is  165,  your  campaign  promise  is  150,  and  your  promise  wins  the  election,  how  many  points  would  you  earn?  

 4. Suppose  that  the  computer  voter’s  favorite  position  is  75.  If  Candidate  A’s  campaign  

promise  is  50  and  Candidate  B’s  campaign  promise  is  125,  which  candidate  would  the  computer  vote  for?  

 5. If  the  computer  voter’s  favorite  position  is  120,  Candidate  C’s  campaign  promise  is  

60  and  Candidate  D’s  campaign  promise  is  150  which  candidate  would  the  computer  vote  for?    

6. Suppose  that  the  computer  voter’s  favorite  position  is  80  and  your  favorite  position  is  20.  If  the  computer  voter’s  choice  in  the  second  stage  is  between  Candidate  E’s  campaign  promise  of  50  and  Candidate  F’s  campaign  promise  of  120,  how  many  points  will  you  earn?    

Online  Appendix:  Instructions  for  Direct  Test  of  Belief  Manipulation  

 Part  2    There  are  20  elections  in  Part  2.  The  basic  rules  for  elections  in  Part  2  are  similar  to  Part  1,  and  the  payoffs  will  be  determined  in  the  same  way  as  before.  However,  there  are  a  few  differences.    In  every  election,  you  will  be  paired  against  one  voter  from  the  other  group,  and  your  task  is  to  vote  in  the  first  stage  election.  Each  pair  of  voters  interacts  separately.  That  is,  your  payoffs  will  depend  only  on  your  actions  and  the  actions  of  the  voter  you  are  paired  against.  The  choices  of  other  pairs  of  voters  will  not  affect  your  payoffs  in  Part  2.  

 Instead  of  choosing  your  own  campaign  promises,  you  will  choose  between  two  promises  that  the  computer  randomly  selects  between  your  favorite  position  and  the  computer  voter’s  favorite  position.  Each  position  in  this  range  is  equally  likely  to  be  selected  as  a  campaign  promise.  For  example,  if  your  favorite  position  is  20  and  the  computer  voter’s  favorite  position  is  80,  then  the  computer  will  randomly  select  two  promises  between  20  and  80  and  you  will  vote  for  one  of  these  two  promises.    Likewise,  the  other  voter  will  choose  between  two  promises  randomly  selected  between  their  favorite  position  and  the  computer  voter’s  favorite  position.  For  example,  if  the  computer’s  favorite  position  is  80  and  the  other  voter’s  favorite  position  is  140,  then  the  computer  will  randomly  select  two  promises  between  80  and  140  and  the  other  voter  will  vote  for  one  of  these  two  promises.    As  before,  the  computer  voter  will  vote  for  the  campaign  promise  closest  to  its  own  favorite  position,  and  the  campaign  promise  selected  in  the  second  voting  stage  determines  everyone’s  payoff  for  that  election.    Are  there  any  questions?  If  you  have  a  question,  please  raise  your  hand.      Instruction  Questions    1. How  are  the  campaign  promises  chosen  in  Part  2?  

 2. If  your  favorite  position  is  40  and  the  computer  voter’s  favorite  position  is  100,  what  is  

the  range  of  values  for  the  two  randomly  selected  promises  YOU  will  choose  from?    

3. If  the  other  voter’s  favorite  position  is  150  and  the  computer  voter’s  favorite  position  is  90,  what  is  the  range  of  values  for  the  two  randomly  selected  promises  the  OTHER  voter  will  choose  from?  

 4. Which  rule  does  the  computer  voter  use  to  determine  the  winner  of  the  election?        

Online  Appendix:  Instructions  for  Direct  Test  of  Belief  Manipulation  

Part  3    There  are  20  elections  in  Part  3.  Instead  of  voting  in  the  first  stage  election,  your  task  is  to  choose  a  campaign  promise  from  1  to  200  (in  the  same  way  as  in  Part  1).  Instead  of  playing  against  another  participant,  you  will  play  against  two  computer  players.  One  computer  player  will  choose  the  other  group’s  position,  and  a  separate  computer  player  will  choose  the  winning  position  in  the  second  voting  stage  just  like  in  Parts  1  and  2.    As  in  Part  2,  the  other  group  will  choose  between  two  randomly  selected  campaign  promises.  Before  choosing  your  promise,  you  will  be  given  a  piece  of  information  about  which  position  the  other  group’s  voter  selected.  Specifically,  you  will  find  out  if  the  voter  selected  the  promise  that  is  closer  to  the  computer  voter’s  favorite  position  or  the  promise  that  is  closer  to  the  other  group’s  favorite  position.  However,  you  will  not  know  the  exact  numerical  value  of  the  position.      For  example,  suppose  the  other  group’s  favorite  position  is  30  and  the  computer  voter’s  favorite  position  is  90  while  the  other  group’s  two  promises  are  40  and  80.  There  are  two  possible  pieces  of  information  you  might  receive:    

• If  the  other  group  chooses  40,  then  you  will  see  a  message  saying  “the  other  voter  chose  the  promise  closer  to  the  OTHER  voter’s  favorite  position”  (since  40  is  closer  to  30  than  80  is).    

• On  the  other  hand,  if  the  other  group  chooses  80,  then  you  will  see  a  message  saying  “the  other  voter  chose  the  promise  closer  to  the  COMPUTER  voter’s  favorite  position”  (since  80  is  closer  to  90  than  30  is).  

 Otherwise,  the  rules  for  determining  your  payoffs  (such  as  the  payoff  formula)  and  for  determining  the  computer  voter’s  vote  are  the  same  as  in  Parts  1  and  2.      Are  there  any  questions?  If  you  have  a  question,  please  raise  your  hand.    Instruction  Questions    1. How  is  the  other  group’s  campaign  promise  determined  in  Part  3?    2. Suppose  the  other  group’s  promises  were  130  and  145,  and  that  you  also  know  that  the  

(second  stage)  computer  voter’s  favorite  position  is  100  and  the  other  group’s  favorite  position  is  160.  Which  of  these  promises  is  closer  to  the  (second  stage)  COMPUTER  voter’s  favorite  position?  

 3. Suppose  the  other  group’s  promises  were  30  and  60,  and  that  you  also  know  that  the  

(second  stage)  computer  voter’s  favorite  position  is  80  and  the  other  group’s  favorite  position  is  20.  Which  of  these  promises  is  closer  to  the  OTHER  group’s  favorite  position?